A baseball is thrown up into the air. The ball's height in feet is modeled by the equation h(t) = -16t2 + 32t + 10. (h = height, t = time in seconds)
Find the maximum height of the ball.
a) 10 feet
b) 2.3 feet
c) 23 feet
d) 26 feet

Question

A baseball is thrown up into the air. The ball's height in feet is modeled by the equation h(t) = -16t2 + 32t + 10. (h = height, t = time in seconds)
Find the maximum height of the ball.
	a)	10 feet
	b)	2.3 feet
	c)	23 feet
	d)	26 feet

anonymous · Answer

oh wait

anonymous · Answer

First, find the time when $\dfrac{dh}{dt}=0$, and then find the height at that time.

anonymous · Answer

it's an upside down parabola so it would be a maximum.  
To find it u can simplify the equation into the turning point one eg y= a(x-b) + c  and the turning point is at (b,c) 

or you could find the x-intercepts and plus them together and then divide by two, after u have got this x value sub in the equation to find ur y value then u will have (x,y) as ur t.p.

anonymous · Answer

simplifying the equation requires completing the square.

anonymous · Answer

@JayDs - It's much quicker with calculus.

anonymous · Answer

(as well as more generally applicable...parabolas are only special cases where you can maximize in that manner)

anonymous · Answer

oh sorry, i haven't learnt calculus yet.

this · Answer

@JayDS its fine :)

this · Answer

therefore....is it A? B? C? D???

anonymous · Answer

@this - Please give the problem an attempt.  We're not just going to solve it for you.

mertsj · Answer

The maximum height of the ball is the y coordinate of the vertex.  The x coordinate of the vertex is :
$$x=\frac{-b}{2a}$$

mertsj · Answer

Find that, plug it into the equation in place of x and find y.  That will be the maximum height of the ball.

this · Answer

i am not getting it plzz help me guys?

anonymous · Answer

@this - What is $\dfrac{dh}{dt}$?

mertsj · Answer

26 feet.  D
 -b/2a=/-32/-32=1
-16(1)+32(1)+10=26
Vertex is (1,26)
high point is 26